Charge Density Study of Two-Electron Four-Center Bonding in a Dimer of Tetracyanoethylene Radical Anions as a Benchmark for Two-Electron Multicenter Bonding

The dimer of the tetracyanoethylene (TCNE) radical anions represents the simplest and the best studied case of two-electron multicenter covalent bonding (2e/mc or pancake bonding). The model compound, N-methylpyridinium salt of TCNE•–, is diamagnetic, meaning that the electrons in two contiguous radicals are paired and occupy a HOMO orbital which spans two TCNE•– radicals. Charge density in this system is studied as a benchmark for comparison of charge densities in other pancake-bonded radical systems. Two electrons from two contiguous radicals indeed form a bonding electron pair, which is distributed between two central ethylene groups in the dimer, i.e., between four carbon atoms. The topology of electron density reveals two bond critical points between the central ethylene groups in the dimer, with maximum electron density of 0.185 e Å–3; the corresponding theoretical value is 0.118 e Å–3.

) are printed in italic in the first column.

S4 Additional details on quantum chemical computations
To ensure that the interacting dimers are in the singlet state, a series of calculations with different electronic state, i.e. singlet, triplet and quintet was performed.Obtained energies (Table S5) indicate that indeed the system is in a singlet state, which is in agreement with previous findings [17].In addition to calculations of dimer, a trimer composed of a dimer and a neighboring TCNE •− radical anion was also computed.The resulting atomic charges (see Table S6) as well as molecular orbital behavior confirmed that binding interaction happens only between two of the three TCNE •− radical anions, the ones that were taken for other dimer-related calculations.

S1
Figure S1 Residual electron density of the multipole refinement at the tetracyanoethylene radical anion (left) and N-methylpyridinium cation (right) planes with all reflections used (top row) and only low-angle reflections (s < 0.7 Å −1 ) used in the refinement (bottom row).Positive density is shown in blue and negative in red; yellow dotted lines represent zero density.Contours are drawn at the 0.05 e Å −1 level.

Figure S2
Figure S2 Residual electron density of the multipole refinement performed on theoretically obtained structure factors.Positive density is shown in blue and negative in red; yellow lines represent zero density.Contours are drawn at the 0.05 e Å −1 level.

Figure
Figure S3 ORTEP-3 drawings of TCNE •− radical anion (left) and N-methylpyridinium cation (right) with atom numbering scheme.Displacement ellipsoids are drawn at the 50% probability and hydrogen atoms are shown as spheres of arbitrary radii.

Figure
Figure S4 Experimental (top row) and theoretical (bottom row) deformation density maps of TCNE •− radical anion (left), and N-methylpyridinium cation (right).Contours are drawn at the 0.05 e Å −3 electron density level; positive density is blue, negative is red and zero contour is drawn as a yellow dotted line.

Figure S6
Figure S6 Crystal packing of 1 viewed in the [100] direction.
Figure S7 Residual electron density in the mean plane of the neutral tetracyanoethylene with all reflections used (left) and only low-angle reflections (s < 0.7 Å −1 ) used (right).Positive density is shown in blue and negative in red; yellow dotted lines represent zero density.Contours are drawn at the 0.05 e Å −1 level.

Figure
Figure S8 ORTEP-3 drawing of a neutral TCNE with atom numbering scheme.Displacement ellipsoids are drawn at the 50% probability level and hydrogen atoms are shown as spheres of arbitrary radii.

Figure S9
Figure S9 Deformation density map of neutral tetracyanoethylene.Contours are drawn at the 0.05 e Å −3 electron density level; positive density is blue, negative is red and zero contour is drawn as a yellow dotted line.

Figure S11
Figure S11HOMO and LUMO molecular orbitals of a TCNE •− radical anions trimer taken from the crystal structure of 1. MO surfaces are drawn at the isovalue of 0.015 au.Alpha refers to positive spin (up), beta to negative spin (down).

Table S1
Topology of electron density in the N-methylpyridinium cation, derived from experimental (regular font) and theoretical (italic) electron-density after multipole refinement.

Table S5
Energy calculations assuming different electronic state for the dimer build of two TCNE •− radical anions

Table S6
Theoretical Bader and Mulliken atomic charges calculated for TCNE •− radical anions involved in stacking interactions.Calculations were done in gas-phase for both dimer or trimer case.
* atomic charges are listed for the radical anion that is in between two other TCNE •− radical anions

Table S7 A
list of structures with TCNE radical anions deposited in the Cambridge Structural Database (CSD).Structures with disordered TCNE moiety are omitted.Different types of interaction are colour-coded: σ-dimers are green, 2e/4c-bonded dimers are yellow, weakly interacting pairs of radicals are light blue, those forming π-complex with a metal are red, stacked charge-transfer system with tetrathiafulvalene is light gray and isolated TCNE's (forming no apparent interactions with other TCNE moieties) are brown.The geometric parameters r and d represent the closest distance between two C atoms of contiguous TCNE moieties and an angle between C=C axes, respectiely.